Sentence examples for discrete frame from inspiring English sources

The perturbation of a discrete frame has been discussed in [3].

A discrete frame is a countable family of elements in a separable Hilbert space which allows for a stable, not necessarily unique, decomposition of an arbitrary element into the expansion of frame elements.

White flowers and white pages (Of a love letter? Of Shakespeare's plays?) created a beautiful but discrete frame for the action.

For more details about discrete frames, see [3].

Of course, this new frame can be useful in function spaces and operator theory to gain some general results that are achieved by g-frames or discrete frames.

The concept of frames (discrete frames) in Hilbert spaces has been introduced by Duffin and Schaeffer [1] in 1952 to study some deep problems in nonharmonic Fourier series.

Actually, continuous frames motivate us to introduce this kind of frames and analogous to continuous frames which are a generalized version of discrete frames, we want to generalize pg-frames in a continuous sense.

Now, we intend to use this space to define a new kind of frames which contain all of continuous and discrete frames; in other words, we will generalize the g-frames to a continuous case that is constructed on the concept of Bochner spaces.

Therefore, ( ∫ Ω ∥ Λ ω x ∥ p d μ 1 p = ∥ F x ∥ = sup ∥ G ∥ q = 1 | 〈 x, T G 〉 | ≤ ∥ T ∥ ∥ x ∥.  □. Similar to discrete frames, the analysis operator has closed range. Lemma 2.10 Let ω ∈ Ω be a Bochner pg-frame for X with respect to { H ω } ω ∈ Ω. Then the operator U defined by (2.3) has closed range.

In psychology, Stroud [57] was one of the first authors to propose the idea of discrete frames or 'moments' underlying consciousness.

One reason people in the Pentagon like Mr Sorley's "A Better War" is that the strategy it discusses was implemented over three to five years, the kind of discrete time frame that military planners can contemplate.